input_case nil$ % Special functions % ----------------- load_package specfn2; % loads both specfn and specfn2 % Gamma function and psi function {gamma(1),gamma(2),gamma(3),gamma(4)}; {gamma(1/2),gamma(3/2),gamma(5/2)}; on rounded; gamma(1/3); on complex; gamma(1+i); off complex,rounded; {psi(1),psi(2),psi(3)}; {psi(1/2),psi(3/2),psi(5/2)}; on rounded; psi(1); psi(1/2); off rounded; % Bessel functions besselj(1/2,x); plot(besselj(0,x),besselj(1,x),besselj(2,x),x=(0 .. 10)); % miscellaneous functions {zeta(2),zeta(4),zeta(6)}; on rounded; {zeta(3),zeta(5)}; off rounded; df(dilog(x),x); {dilog(0),dilog(1),dilog(2)}; on rounded; dilog(3); off rounded; df(ei(x),x); on rounded; ei(1); off rounded; df(erf(x),x); erf(0); limit(erf(x),x,infinity); % Legendre polynomials and spherical harmonics for l:=0:3 collect legendrep(l,x); for l:=1:3 do write for m:=1:l collect legendrep(l,m,x); for l:=0:3 do write for m:=0:l collect sphericalharmonicy(l,m,theta,phi); % miscellaneous polynomials for n:=0:3 collect hermitep(n,x); for n:=0:3 collect laguerrep(n,x); for n:=1:3 do write for m:=1:n collect laguerrep(n,m,x); % generalized hypergeometric function hypergeometric({},{},x); hypergeometric({-a},{},x); hypergeometric({1,1},{2},x); end;